This MCQ module is based on: Chapter 4 Exercises and Summary
TOPIC 13 OF 22
Chapter 4 Exercises and Summary
🎓 Class 8
Mathematics
CBSE
Theory
Ch 4 — Quadrilaterals
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Chapter 4 Exercises and Summary
Targeting Class 8 level in Geometry, with Basic difficulty.
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4.6 Kite — A Special Quadrilateral
A kite? is a quadrilateral with two non-overlapping adjacent pairs of sides having the same length. One diagonal bisects the other and the angle at each vertex through which it passes.
Kite ABCD: AB = AD and CB = CD; diagonals meet at right angles.
Exercises (End-of-Chapter)
Q1. A quadrilateral having three right angles is a rectangle. True or false? Justify.
True. The sum of interior angles of a quadrilateral is 360°. If three are 90°, the fourth must be 360 − 270 = 90°. Hence all four are 90° → rectangle.
Q2. A quadrilateral in which the diagonals bisect each other is a parallelogram.
True. Using SAS, the two pairs of triangles formed are congruent, giving opposite sides equal and parallel.
Q3. A quadrilateral whose diagonals are perpendicular to each other is a rhombus.
False in general. Perpendicular diagonals alone give a kite, not necessarily a rhombus. A rhombus requires the diagonals to also bisect each other.
Q4. A quadrilateral whose diagonals are perpendicular to each other AND bisect each other is a rhombus.
True. With these two properties, all four sides come out equal.
Q5. A quadrilateral in which the opposite angles are equal is a parallelogram.
True. From angle-sum = 360° and opposite angles equal, adjacent angles become supplementary, which makes opposite sides parallel.
Q6. A quadrilateral in which all the angles are equal is a rectangle.
True. All angles equal ⇒ each = 90° ⇒ rectangle.
Q7. Isosceles trapeziums are parallelograms.
False. An isosceles trapezium has only one pair of parallel sides; its non-parallel sides are equal but not parallel.
Q8. In rhombus ABCD, ∠A = 72°. Find ∠B, ∠C, ∠D.
∠C = 72°; ∠B = ∠D = 108° (adjacent angles supplementary).
Q9. The diagonals of a rectangle have length 10 cm each and intersect at O. Find OA.
Diagonals bisect each other, so OA = 5 cm.
Q10. In a parallelogram PQRS, ∠P = (3x + 15)° and ∠Q = (5x − 25)°. Find x.
Adjacent angles are supplementary: \((3x+15) + (5x-25) = 180\) ⇒ \(8x - 10 = 180\) ⇒ \(8x = 190\) ⇒ \(x = 23.75°\).
Activity: Quadrilateral Family Tree Poster
L6 Create
Materials: Chart paper, coloured markers, set-square, ruler.
- Draw a large Venn diagram covering: Quadrilateral → Trapezium → Parallelogram → Rectangle/Rhombus → Square.
- Place exactly one example shape in each region.
- Label each region with its defining property.
- Present your poster to class.
Quadrilateral ⊃ Trapezium ⊃ Parallelogram ⊃ {Rectangle, Rhombus}; Square = Rectangle ∩ Rhombus.
Competency-Based Questions
Scenario: A civil engineer is designing a decorative floor tile. Four tile shapes are being considered: (A) square, (B) rhombus (non-square), (C) rectangle (non-square), (D) isosceles trapezium.
Q1. Which tiles will tessellate (tile a plane without gaps) using the same tile?
L3 ApplyAll four tessellate — any quadrilateral tessellates the plane because the four angles around any common vertex can be arranged to sum to 360°.
Q2. Analyse: which shape uses the least cutting waste from a large rectangular slab of stone?
L4 AnalyseRectangles (including squares) waste nothing — they align with the slab's own axes. Rhombi and trapezia leave triangular off-cuts.
Q3. Evaluate: A tile must look "the same" when flipped horizontally. Which of A–D qualify?
L5 EvaluateSquare and rhombus have line symmetry along both diagonals. Rectangle has line symmetry through midpoints of opposite sides. Isosceles trapezium has one line of symmetry. All four qualify, but non-isosceles trapezium would not.
Q4. Design a composite pattern using tiles A and B (square + rhombus) that covers a 2 m × 2 m floor. Describe the arrangement.
L6 CreateSample design: Lay 20×20 cm squares in rows. Between every 4 squares (at the vertices), place a 20-cm-diagonal rhombus rotated 45°. This creates a "star pattern" — both shapes fit without gaps because their angles around each vertex sum to 360°.
Assertion–Reason Questions
A: A quadrilateral whose diagonals bisect each other at right angles is a square.
R: Such a quadrilateral is a rhombus.
R: Such a quadrilateral is a rhombus.
(d) — A is false (could be a non-square rhombus). R is true.
A: Every rectangle is a trapezium.
R: A trapezium needs at least one pair of parallel sides.
R: A trapezium needs at least one pair of parallel sides.
(a) — A rectangle has two pairs of parallel sides, satisfying the "at least one" condition of a trapezium.
Summary
- A rectangle is a quadrilateral in which the angles are all 90°. Properties: opposite sides equal; opposite sides parallel; diagonals equal and bisect each other.
- A square is a quadrilateral in which the angles are all 90° and all the sides are of equal length. Properties: opposite sides are parallel; the diagonals of a square are equal in length and bisect each other at 90°; the diagonals of a square bisect the angles of the square.
- A parallelogram is a quadrilateral in which opposite sides are parallel. Properties: opposite sides of a parallelogram are equal; adjacent angles add up to 180°, and the opposite angles are equal; diagonals of a parallelogram bisect each other.
- A rhombus is a quadrilateral in which all sides have the same length. All the properties of a parallelogram apply. In a rhombus, the adjacent angles add up to 180°, and the opposite angles are equal. The diagonals of a rhombus bisect each other at right angles.
- A kite is a quadrilateral with two non-overlapping adjacent pairs of sides having the same length.
- A trapezium is a quadrilateral having at least one pair of parallel opposite sides.
- The sum of the angle measures in a quadrilateral is 360°.
Quadrilateral family Venn diagram — page 110
Frequently Asked Questions
What exercises are in Class 8 Chapter 4?
Chapter 4 exercises include identifying quadrilateral types, computing missing sides/angles using properties, proving that a figure is a parallelogram/rhombus, and applying the Pythagorean theorem to diagonals. NCERT Class 8 Ganita Prakash Part 1 covers all key concepts.
How to solve a quadrilateral proof?
State what is given and what to prove. Use known properties (opposite sides equal, angles equal, diagonals bisect) to build a logical chain. Cite each property used. End with 'hence proved'. NCERT Class 8 Chapter 4 exercises practise this structure.
What is the summary of Chapter 4?
Key ideas: quadrilaterals have many types; squares and rectangles have four right angles; parallelograms have parallel opposite sides; rhombuses have equal sides with perpendicular diagonals; trapeziums have one pair of parallel sides. NCERT Class 8 Ganita Prakash Part 1 Chapter 4.
Why do quadrilaterals matter in higher maths?
Quadrilaterals underpin coordinate geometry, trigonometry, area computations, and engineering design. Understanding their properties is essential for Classes 9 and 10 geometry. NCERT Class 8 Chapter 4 is the springboard.
How do angle sums work in quadrilaterals?
Every quadrilateral's interior angles sum to 360°. This follows by dividing it into two triangles along a diagonal (each triangle sums to 180°). NCERT Class 8 Ganita Prakash Part 1 Chapter 4 exercises apply this frequently.
When is a parallelogram a rhombus?
A parallelogram is a rhombus when all four sides are equal, or equivalently when the diagonals are perpendicular. Either condition guarantees rhombus status. NCERT Class 8 Chapter 4 uses both tests in exercises.
Frequently Asked Questions — Quadrilaterals
What is Chapter 4 Exercises and Summary in NCERT Class 8 Mathematics?
Chapter 4 Exercises and Summary is a key concept covered in NCERT Class 8 Mathematics, Chapter 4: Quadrilaterals. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Chapter 4 Exercises and Summary step by step?
To solve problems on Chapter 4 Exercises and Summary, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 8 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 4: Quadrilaterals?
The essential formulas of Chapter 4 (Quadrilaterals) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Chapter 4 Exercises and Summary important for the Class 8 board exam?
Chapter 4 Exercises and Summary is part of the NCERT Class 8 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Chapter 4 Exercises and Summary?
Common mistakes in Chapter 4 Exercises and Summary include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Chapter 4 Exercises and Summary?
End-of-chapter NCERT exercises for Chapter 4 Exercises and Summary cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 4, and solve at least one previous-year board paper to consolidate your understanding.
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